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I always thought rule-based was synonymous with logic-based AI. Logic has axioms and rules of inference, whereas rule-based AI has a knowledge base (essentially, axioms) and if-then rules to create new knowledge (essentially inference rules).

But in their famous article What is a Knowledge Representation?, Davis, Shrobe and Szolovits seem to imply that they are not:

Logic, rules, frames, and so on, embody a viewpoint on the kinds of things that are important in the world. Logic, for example, involves a (fairly minimal) commitment to viewing the world in terms of individual entities and relations between them. Rule-based systems view the world in terms of attribute-object-value triples and the rules of plausible inference that connect them, while frames have us thinking in terms of prototypical objects.

Is this only saying that rule-based are propositional, whereas logic-based is usually meant to mean predicate logic? Or is there more to it than this?

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Rule-based systems cover a wide range of systems. Some make use of boolean if/then/else rules, others may use weighting or even probabilistic inference. Some operate on frames, some on java objects, some on propositions that can be formulated in predicate logic. An example of a popular rule system is Drools.

Some rule systems can be expressed as a subset of predicate logic. For example, SWRL is a W3C standard rule language that extends OWL Description Logic (DL) with horn rules. Both OWL-DL and SWRL are expressible in first-order predicate logic. However, not all rule languages are directly expressible in this way, as rule languages encompass such a range of semantics. Even in cases like Prolog, there are subtleties. Pure Prolog is a subset of FOL, but actual existing Prolog implementations are not FOL subsets (e.g. order of precedence matters).

The W3C Rules Interchange Format (RIF) working group has done a lot of work attempting to unify these different perspectives. I'm not sure the best place to start to see a summary, but you can see some useful material on the group charter page.

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